Question

Factor the given polynomial. Factor out -1 if the leading coefficient is negative.

7x²y - 35xy² + 14xy
A. 7x²y - 35xy² + 14xy
B. The polynomial is prime.
C. 7x(x - 5y + 2)
D. 7xy(x - 5y + 2)

Answer 1

The factored form of the polynomial 7x²y - 35xy² + 14xy is 7xy(x - 5y + 2), which corresponds to option D. The factoring process involves finding the greatest common factor and checking the answer by multiplying the factors back together.

Step-by-step explanation:

The question involves factoring a polynomial. To factor the given polynomial 7x²y - 35xy² + 14xy, we first look for the greatest common factor (GCF) of all the terms. Here, each term contains a factor of 7, x, and y. Factoring out the GCF 7xy gives us:

7xy(x - 5y + 2)

Thus, the factored form of the polynomial is 7xy(x - 5y + 2), which corresponds to option D.

To check if the answer is reasonable, we can multiply the factors back together:

7xy * x = 7x²y
7xy * -5y = -35xy²
7xy * 2 = 14xy

Combining these terms, we get the original polynomial, confirming that our factored form is correct.